$\int \sqrt[3]{x^7}\,dx=$ $+C$
Answer: At first it might seem as if we can't apply any rule we've learned to find the indefinite integral of a radical function. However, remember that any radical can be rewritten as a rational power. $\int \sqrt[3]{x^7}\,dx=\int x^{^{\frac73}}\,dx$ Now we can integrate using the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int \sqrt[3]{x^7}\,dx&=\int x^{^{\frac73}}\,dx \\\\ &=\dfrac{x^{^{\frac73+1}}}{\dfrac73+1}+C \\\\ &=\dfrac{3}{10}x^{^{\frac{10}{3}}}+C \end{aligned}$ In conclusion, $\int \sqrt[3]{x^7}\,dx=\dfrac{3}{10}x^{^{\frac{10}{3}}}+C$